| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 4032.1-a1 |
4032.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{8} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.882282413$ |
$1.552362152$ |
2.070673566 |
\( -\frac{48284377}{189} a + \frac{36331342}{567} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 4 a + 53\) , \( -96 a + 72\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(4a+53\right){x}-96a+72$ |
| 4032.1-a2 |
4032.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{2} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.882282413$ |
$3.104724304$ |
2.070673566 |
\( \frac{219127}{7} a - \frac{1223602}{21} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4 a - 8\) , \( 3 a + 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-8\right){x}+3a+14$ |
| 4032.1-a3 |
4032.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{4} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.441141206$ |
$3.104724304$ |
2.070673566 |
\( \frac{4009}{21} a + \frac{3310}{63} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -a + 3\) , \( -2 a + 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-a+3\right){x}-2a+4$ |
| 4032.1-a4 |
4032.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{10} \cdot 3^{2} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.220570603$ |
$3.104724304$ |
2.070673566 |
\( -\frac{166231}{49} a + \frac{1158718}{147} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -4 a - 2\) , \( -3 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-4a-2\right){x}-3a+1$ |
| 4032.1-b1 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{10} \cdot 3^{4} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.983354618$ |
1.499275166 |
\( \frac{863944673}{63} a - \frac{2480308966}{63} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -36 a + 59\) , \( -27 a - 145\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-36a+59\right){x}-27a-145$ |
| 4032.1-b2 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{17} \cdot 3^{2} \cdot 7^{8} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.991677309$ |
1.499275166 |
\( -\frac{70011793}{7203} a - \frac{50355456}{2401} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -21 a + 94\) , \( -214 a - 28\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-21a+94\right){x}-214a-28$ |
| 4032.1-b3 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.983354618$ |
1.499275166 |
\( -\frac{172799}{441} a + \frac{48094}{441} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a + 4\) , \( -13 a + 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-6a+4\right){x}-13a+14$ |
| 4032.1-b4 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.983354618$ |
1.499275166 |
\( \frac{839201}{189} a + \frac{38270}{567} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a - 6\) , \( -20 a + 15\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-6\right){x}-20a+15$ |
| 4032.1-b5 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{16} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.991677309$ |
1.499275166 |
\( -\frac{78717967}{15309} a + \frac{227060962}{45927} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -15 a - 56\) , \( 22 a + 211\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-15a-56\right){x}+22a+211$ |
| 4032.1-b6 |
4032.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{17} \cdot 3^{2} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.983354618$ |
1.499275166 |
\( \frac{13784383}{21} a - \frac{1921824}{7} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a - 38\) , \( 112\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-a-38\right){x}+112$ |
| 4032.1-c1 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{16} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.304790221$ |
1.843198006 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -170 a - 68\) , \( -3689 a + 1302\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-170a-68\right){x}-3689a+1302$ |
| 4032.1-c2 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a + 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(5a+2\right){x}$ |
| 4032.1-c3 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{8} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.219160885$ |
1.843198006 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -20 a - 8\) , \( -17 a + 6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-20a-8\right){x}-17a+6$ |
| 4032.1-c4 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{16} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -195 a - 78\) , \( 1530 a - 540\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-195a-78\right){x}+1530a-540$ |
| 4032.1-c5 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( -\frac{2940226}{21} a + \frac{5920433}{21} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 11 a - 20\) , \( -38 a + 27\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(11a-20\right){x}-38a+27$ |
| 4032.1-c6 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -6 a + 24\) , \( -21 a - 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-6a+24\right){x}-21a-18$ |
| 4032.1-c7 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{4} \cdot 7^{8} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.609580442$ |
1.843198006 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -245 a - 98\) , \( -2312 a + 816\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-245a-98\right){x}-2312a+816$ |
| 4032.1-c8 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.304790221$ |
1.843198006 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -3920 a - 1568\) , \( -144755 a + 51090\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-3920a-1568\right){x}-144755a+51090$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
